Label-Free Cellular Manipulation and Sorting Via Biocompatible Ferrofluids

ABSTRACT

A device for separating a sample of cells suspended in a bio-compatible ferrofluid is described. The device includes a microfluidic channel having a sample inlet, at least one output, and a length between the sample inlet and the at least one output, wherein a sample can be added to the sample inlet and flow along the length to the at least one outlet. The device includes a plurality of electrodes, wherein the microfluidic channel length transverses the plurality of electrodes, and further includes a power source for applying a current to the plurality of electrodes to create a magnetic field pattern along the length of the microfluidic channel. The present invention also includes a method for separating at least one cell type. The method includes the steps of suspending cells in a bio-compatible ferrofluid to form a sample, passing the sample through a microfluidic channel that transverses a plurality of electrodes, applying a current to the plurality of electrodes to create a magnetic field pattern along the length of the microfluidic channel, and sorting the ceils into at least one output channel based on a variation of at least one of cell size, shape and elasticity.

BACKGROUND OF THE INVENTION

Early diagnosis of diseases involving rare cells in blood (such asmetastatic cancer or low-level bacteremia) and accurate monitors ofcertain genetic conditions (such as sickle cell anemia) require rapidand accurate separation, sorting, and direction of target cell typestoward sensor surface. In that regard, cellular manipulation,separation, and sorting are increasingly finding application potentialwithin various bioassays so the context of cancer diagnosis (Dittrich etal., 2006: Nat Rev Drug Discovery 5:210-218), pathogen detection (Beyoret al., 2008, Biomed Microdevices 10:909-917), and genomic testing(Kamei et al. 2005, Biomed Microdevices 7:147-152; Cheong el al., 2008,Lab Chip 8:810-813).

A variety of contactless micromanipulation methods exist, includingoptical tweezers (Ashkin et al., 1987, Nature 330:769-771; Chiou et al.,2005, Nature 436:370-372), dielectrophoresis (DEP) (Hughes, 2002,Electrophoresis 23:2569-2582), magnetic bead-based separators (Lee etal., 2001, Appl Phys Lett 79:3308-3310; Yan et al., 2004, Phys Rev E70:011905), and deterministic hydrodynamics (Davis et al., 2006, ProcNatl Acad Sci USA 103:14779-14784). However, most existing methods havebeen unable to reliably achieve fast speed, high throughput andresolution, simultaneously with low costs (Dufresne et al., 1998, RevSci Instrum 69:1974-1977; Kremser et al., 2004, Electrophoresis25:2282-2291; Cabrera et al., 2001 Electrophoresis 22:355-362). Opticaltweezers offer high resolution and sensitivity for manipulating singlecells, although such manipulation may cause sample heating (Liu et al.,1995, Biophys J 68:2137-2144), and is typically limited to a very smallarea (Ashkin et al., 1987, Science 235:1517-1520). Holographic schemeshave recently extended the reach of optical tweezers to several tens ofcells simultaneously (Applegate et al., 2004, Optical Express12:4390-4398), although the overall throughput remains quite low.Schemes based on electric fields, such as DEP, offer the potential torealize integrated, cost-effective devices for the simultaneousmanipulation of multiple cells; nevertheless, their performance dependssensitively on the electrical properties of the specific liquid medium,the particle shape, and its effective dielectric constant (Pethig etal., 1997, Trends Biotechnol 15:426-432). DEP device operating regimesand the working ionic medium need to be carefully optimized for eachdifferent cell type so as to reach workable compromise between the needto reduce heating (Menachery et al., 2005, NanoBiotechnology152:145-149; Muller, et al., 2003, IEEE Eng Biol Med Mag 22:51-61) andminimize cell polarization (Sebastian et al., 2006, J Micromech Microeng16:1769-1777). Using functionalized magnetic beads to separate targetmolecules and cells overcomes these challenges through the use ofmagnetic fields instead of electric. However, the downside of thistechnique is the lengthy incubation time and wash cycles, and thedifficulty of removing the label post priori (Gijs 2004, MicrofluidicsNanofluidics 1:22-40). The deterministic hydrodynamics approach, asdemonstrated by Davis et al. (Davis et al., 2006, Proc Natl Acad Sci USA103:14779-14784), is capable of achieving high resolution of separationwithout the use of any electromagnetic fields. However, high throughputwith this device requires high-resolution lithography on a large area,keeping the cost per device high.

Most common applications of ferrofluids in biomedicine involve highlydilute colloidal suspensions of magnetic nanoparticles. Their widestcommercial use is as MRI contrast agents (Kim et al., 2005, J Magn MagnMater 289:328-330). When properly coated with targeting antibodies, theycan also be used in hyperthermia therapy for cancer or as sensors todetect pathogens (Scherer et al., 2005, Brazilian J Phys 45:718-727).While these advances in the use of ferrofluids provide manyopportunities in medicine and diagnostics, there remains a need in theart for a microfluidic platform that uses biocompatible ferrofluids forthe controlled manipulation and rapid separation of both microparticlesand live cells. The present invention satisfies this need.

SUMMARY OF THE INVENTION

A device for separating a sample of particles suspended in abiocompatible ferrofluid is described. The device includes amicrofluidic channel having a sample inlet, at least one output, and alength between the sample inlet and the at least one output, wherein asample can be added to the sample inlet and flow along the length to theat least one outlet. The device includes a plurality of electrodes,wherein the microfluidic channel length transverses the plurality ofelectrodes, and further includes a power source for applying a currentto the plurality of electrodes to create a magnetic field pattern alongthe length of the microfluidic channel. In one embodiment, the spacingbetween electrodes is gradually increased. In another embodiment, thespacing between electrodes is gradually decreased. In anotherembodiment, the plurality of electrodes comprise at least one electrodelayer. In another embodiment, the plurality of electrodes comprises aplurality of electrode layers. In another embodiment, the plurality ofelectrode layers is in a substantially orthogonal pattern. In anotherembodiment, the plurality of electrodes comprises a pattern ofconcentric circles. In another embodiment, the walls of the microfluidicchannel length include a pocketed, a ridged, a grooved, a trenched or asloped region. In another embodiment, the microfluidic channel lengthtransverses at least a portion of the plurality of electrodes at anangle between about 1-90 degrees. In another embodiment, the particlesare living cells.

Also described is a system for separating at least one target from asample suspended in a biocompatible ferrofluid. The system includes amicrofluidic channel having a sample inlet, at least one output, and alength between the sample inlet and the at least one output, wherein asample can be added to the sample inlet and flow along the length to theat least one outlet. The system also includes a plurality of electrodes,wherein the microfluidic channel length transverses the plurality ofelectrodes, and further generates a magnetic field pattern along thelength of the microfluidic channel when a current is applied to theelectrodes. The system further includes at least one target in a samplesuspended in a biocompatible ferrofluid, wherein the at least one targetis separated from the remaining sample as the at least one target passesalong at least a portion of the microfluidic channel length. In oneembodiment, the biocompatible ferrofluid comprises a suitable amount ofionic species to control the osmotic pressure on the cells to promotecell sustainability. In another embodiment, the biocompatible ferrofluidcomprises a citrate concentration of between about 5-200 mM. In anotherembodiment, the biocompatible ferrofluid comprises a citrateconcentration of about 40 Mm. In another embodiment, the biocompatibleferrofluid has a pH of about 7.4. In another embodiment, the at leastone target is separated based on target size. In another embodiment, theat least one target is separated based on target shape. In anotherembodiment, the at least one target is separated based on targetelasticity. In another embodiment, the target is separated by beingdirected to a selected outlet. In another embodiment, the target istrapped based on the spacing of electrodes. In another embodiment, theat least one target is a cell. In another embodiment, the at least onetarget is a particle.

Also described is a method for separating at least one cell type. Themethod includes the steps of suspending two or more cell types in abiocompatible ferrofluid to form a sample, passing the sample through amicrofluidic channel that transverses a plurality of electrodes,applying a current to the plurality of electrodes to create a magneticfield pattern along the length of the microfluidic channel, and sortingthe cells into at least one output channel based on a variation of atleast one of cell size, shape and elasticity. In one embodiment, thecells are separated at an efficiency of at least about 90%. In anotherembodiment, the size resolution is separating is less than about 10 μm.In another embodiment, the cells are separated in less than about 1minute.

BRIEF DESCRIPTION OF THE DRAWINGS

For the purpose of illustrating the invention, there are depicted in thedrawings certain embodiments of the invention. However, the invention isnot limited to the precise arrangements and instrumentalities of theembodiments depicted in the drawings.

FIG. 1, comprising FIGS. 1A-1D, illustrate a ferromicrofluidic deviceand particle manipulation platform. FIG. 1A is a schematic of theexperimental setup displaying the microfluidic channel and theunderlying electrodes (not drawn to scale). Two output channels from anamplifier provide sinusoidal currents (I₁ and I₂) phase-locked 90° withrespect to each other. The neighboring electrodes on the substrate areconnected in a manner to carry sinusoidal currents in quadrature andsupport a traveling wave magnetic field within the microfluidic channel.The magnetic field gradient generated pushes the nonmagneticmicrospheres or cells within the ferromicrofluidic channel up and intothe gap between electrodes (i); the traveling field also causes thecells to rotate and roll along the channel ceiling, resulting incontinuous translation along the length of the channel at frequenciesabove a threshold (ii). The resulting microparticle motion is observedwith an upright microscope from above and captured with a CCD camera at18 frames per second for further analysis. FIG. 1B depicts a COMSOLsimulation of a magnetic field (dark arrows) and magnitude of magneticflux density (color) across the cross-section of the ferromicrofluidicdevice at a given instant in time. Fainter arrows depict the field atever 30° within one period. Simulation is for 12-A peak-to-peak currentinput at 1,670 Hz. FIG. 1C is a graph of computed force and torque on a6-μm diameter microsphere along the length of the microchannel with 7-Apeak-to-peak input excitation at 4.6 kHz. FIG. 1D is a graph of computedmagnetic force and torque as a function of frequency for the sameparticle located between electrodes on the channel ceiling. Inputcurrent amplitude is 7 A peak to peak; assumed slip factor for allsimulations depicted here is 1.

FIG. 2, comprising FIGS. 2A-2C characterizes biocompatible ferrofluid.FIG. 2A is a graph depicting the distribution of cabaltferritenanoparticle sizes within the ferrofluid, as obtained by TEM, Meannanoparticle core diameter is 11.3±4.4 nm. (Scale bar: 50 nm.) FIG. 2Bis a graph depicting ac susceptibility and dc magnetization curve(Inset) of the ferrofluid. A fit to the ac susceptibility data assuminga log-normal size distribution indicates moderate particle aggregationwith a mean hydrodynamic diameter of 72.5 nm. FIG. 2C is a chartdepicting live cell count vs. citrate concentration. As shown herein, 40mM citrate concentration (stabilized with citric acid to yield a pH of7.4) is found to be optimum for cell viability and ferrofluid stabilitycombined. The dashed line shows the cell count in the original bloodsample. Count 3 corresponds to cells spending ≈1 h in the citratesolution.

FIG. 3, comprising FIGS. 3A and 3B, is a demonstration of particlevelocity as a function of input frequency and current amplitude. FIG. 3A(middle) is a spatial distribution of instantaneous average x-velocitiesfor 6-μm-diameter particles at 7-A input current amplitude (peak topeak) at two different frequencies. Because of repulsive forces frommagnetic field gradients, microparticles either slow down or completelystop in between electrodes. Zero crossings with negative slopecorrespond to stable equilibrium points (i.e., particle trapping); FIG.3A (top) shows at 10 Hz, particle trajectories terminate in betweenelectrodes, resulting in trapping. FIG. 3A (bottom) shows at 4,640 Hz,particles move continuously throughout the length of the channel. Thisis the regime where magnetic torque from the locally rotating componentof the traveling wave dominates over the repulsive forces. The blackdots at the end of each trajectory indicate where particles eventuallystop. FIG. 3B shows that above a critical frequency (f_(c)), the 6-μmmicrospheres roll continuously along the top channel surface withoutgetting trapped.

FIG. 4, comprising FIGS. 4A-4D, are illustrative of frequency-dependentparticle separation. FIG. 4A depicts the particle size dependence ofcritical frequency (f_(c)). Discrete f_(c) values for differentdiameters of particles enable size-based separation by tuning to theright frequency. The solid curve corresponds to the simulation resultwith a slip factor of 1 and a particle-wall gap of 1 nm. FIG. 4B depictsthe average manipulation speed as a function of input frequency for twodifferent particle sizes; 2.2- and 9.9-μm particles can be separated at400 Hz. FIG. 4C is a fluorescent microscopy image from a section of themicrofluidic channel containing 2.2- and 9.9-μm microspheres randomlydispersed within the channel right before the excitation. Vertical linesindicate electrode borders. FIG. 4D is a snapshot of the channel fromthe same location as in FIG. 4C, 45 seconds after the excitation (6 Apeak to peak, 400 Hz) is turned on. The 9.9-μm particles quicklylocalize within the nearest spring between electrodes, whereas 97% ofthe 2.2-μm microspheres continuously travel from right to left withoutbeing trapped. Almost all of the smaller microspheres within the fieldof view in FIG. 4D have entered from the right as a fresh batch.

FIG. 5, comprising FIGS. 5A and 5B, depict cellular separation withbacteria and blood cells. FIG. 5A depicts the spatial distribution ofx-velocities at 200 Hz in a sample containing E. coli bacteria and redblood cells. At this frequency, most red blood cells are trapped betweenthe electrodes (indicated by their zero local speeds), whereas E. colican slowly but continuously move through that region. Fluctuations inthe red blood cell data are statistical in nature, as explained herein.FIG. 5B depicts sickle cell separation. Sickle cells, which have anelongated shape and altered elasticity compared with normal red bloodcells, are trapped and concentrated between the electrodes, whereas thehealthy cells are still able to circulate within the microfluidicchannel at 300 Hz. Electrode spacing of the device in FIG. 5A isdifferent from that in FIG. 5B, resulting in different f_(c) s for redblood cells within each channel.

FIG. 6, comprising FIGS. 6A-6C, FIG. 6A depicts microparticle averagespeed, normalized by the square of the current amplitude (peak-to-peak)and to the maximum value at 5 A, depicted as a function of excitationfrequency. Particle velocities are proportional to the square of currentuntil about 7 A. FIG. 6B depicts the average velocity vs. frequency at 6A peak-to-peak for 9.9 μm microspheres travelling over electrodes withdifferent spacings. A smaller spacing leads to higher particle velocityand a smaller critical frequency. FIG. 6C depicts a conceptual sketch ofa microparticle sorter based on the effect observed in 6C. At a givenexcitation frequency, smaller spacings trap larger particles, whileletting smaller ones pass through. Eventually, even the smallestparticles can be trapped in the larger gaps. Here, it is assumed thatparticles move from left to right, and the channel over the electrodesdepicted is initially cell-free.

FIG. 7, comprising FIGS. 7A and 7B depict alternative embodiments of theelectrode and channel components of the separating device. FIG. 7Adepicts electrode formations of 100, 150, 200 and 300 μm spacing in thechannel. FIG. 7B depicts channel formations of between about 0.17-0.19cm, and having four inlets and four outlets.

FIG. 8, comprising FIGS. 8A and 8B, depict alternative embodiments ofelectrode patterns. FIG. 8A depicts a multi-layer electrode pattern thatis substantially orthogonal FIG. 8B depicts electrodes in a pattern ofconcentric circles.

FIG. 9 depicts a continuous flow device allowing a sample suspendedwithin the ferrofluid to enter the device inlet and pass through theseparation chamber, and exit via multiple outlets designed for capturingparticles of a particular size. The 2 μm particles flow to outlet A, the5 μm particles flow to outlet B, and the remaining sample flows to awaste outlet C. The flow device depicted in FIG. 9 is thus suitable forsorting two or more particle types based on one or a combination ofsize, shape and elasticity.

DETAILED DESCRIPTION

The present invention relates to a microfluidic platform that usesbiocompatible ferrofluids for the controlled manipulation and rapidseparation of both microparticles and live cells. More particularly, thepresent invention relates to the high-throughput manipulation,label-free sorting and separating of cells via a concentrated ferrofluidthat is bio-compatible. Bio-compatibility of the ferrofluid is based onan effective balance, or concentration, of ionic surfactant such ascitrate. Bio-compatibility generally requires a neutral pH, a sufficientosmotic pressure on the cells, and a stable ferrofluid (too much ioniccontent destabilizes the suspension). This low-cost platform exploitsdifferences in particle size, shape, and elasticity to achieve rapid andefficient separation. Using microspheres, size-based separation isdemonstrated with about separation efficiency and sub-10-μm resolutionin less than about 45 seconds. The present invention also provides forthe continuous manipulation and shape-based separation of live red bloodcells from sickle cells and bacteria. These demonstrations highlight theability of ferromicrofluidics to significantly reduce incubation timesand increase diagnostic sensitivity in cellular assays through rapidseparation and delivery of target cells to sensor arrays.

Definitions

Unless defined otherwise, ALL technical and scientific terms used hereinhave the same meaning as commonly understood by one of ordinary skill inthe art to which this invention belongs. Although any methods andmaterials similar or equivalent to those described herein can be used inthe practice or testing of the present invention, the preferred methodsand materials are described.

As used herein, each of the following terms has the meaning associatedwith it in this section.

The articles “a” and “an” are used herein to refer to one or to morethan one (i.e., to at least one) of the grammatical object of thearticle. By way of example, “an element” means one element or more thanone element.

“About” as used herein when referring to a measurable value such as anamount, a temporal duration, and the like, is meant to encompassvariations of ±20% or ±10%, more preferably ±5%, even more preferably±1%, and still more preferably ±0.1% from the specified value, as suchvariations are appropriate to perform the disclosed methods.

Throughout this disclosure, various aspects of the invention can bepresented range format. It should be understood that the description inrange format is merely for convenience and brevity and should not beconstrued as an inflexible limitation on the scope of the invention.Accordingly, the description of a range should be considered to havespecifically disclosed all the possible subranges as well as individualnumerical values within that range. For example, description of a rangesuch as from 1 to 6 should be considered to have specifically disclosedsubranges such as from 1 to 3, from 1 to 4, from 1 to 5 ,from 2 to 4,from 2 to 6, from 3 to 6 etc., as well as individual numbers within thatrange, for example, 1, 2, 2.7, 3, 4, 5, 5.3, 6 and any whole and partialincrements therebetween. This applies regardless of the breadth of therange.

Separation Systems and Devices

In one aspect, the present invention includes a microfluidic system,based on ferrohydrodynamics for the label-free manipulation andseparation of cells and microorganisms within biocompatible ferrofluids.In one embodiment, the system includes a water-based ferrofluid is usedas a uniform magnetic environment that surrounds the cells or otherparticles within a microfluidic channel. Cells and other nonmagneticparticles within the ferrofluid act as “magnetic voids” (Kashevsky,1997, Phys Fluids 9:1811-1818), in a manner analogous to electronicholes in a semiconductor. An externally applied magnetic field gradientcan attract magnetic nanoparticles, which causes nonmagneticmicroparticles or cells to be effectively pushed away (Rosensweig R E(1997) Ferrohydrodynamics (Dover, N.Y.); Odenbach S (2002) Ferrofluids:Magnetically Controllable Fluids and Their Applications (Springer,N.Y.)). Recently, this principle has been applied to capture nonmagneticmicrobeads between magnetic film islands in a microchannel filled withferrofluid (Yellen et a., 2005, Proc Natl Acad Sci USA 102:8860-8864).In contrast to this, the present invention can utilize a microfluidicdevice with integrated copper electrodes that carry currents to generateprogrammable magnetic field gradients locally, as depicted in FIG. 1A.

For example, the particle manipulation device of the present inventionincludes two primary components; 1) a microfluidic channel; and 2)underlying electrodes. At least one electrode layer may sit atop astandard, insulated metal substrate. For example, an aluminium substratecoated with an insulating polymer may be used, which allows efficientheat sinking, and enable AC currents up to 10 A at low voltages throughthe electrodes. In one exemplary embodiment, a single electrode layer isused, as may be seen in FIG. 1A. In other exemplary embodiments,multiple electrode layers are used to provide multi-dimensional control,for example, such as the orthogonal electrode layers depicted in FIG.8A. Within a given electrode layer, the electrodes may be about 30 μmhigh, about 300 μm wide and about 2 cm in length. In alternativeembodiments, the electrodes within a given layer may range anywhere fromabout 5-100 μm high, about 0.01-1 mm wide, and about 0.1-10 cm inlength, and any whole or partial increments therebetween. Thus, itshould be appreciated that the size of electrodes utilized is notlimited, and can vary across multiple electrode layers. Further, theelectrodes may include any area shape, curvature or pattern, and mayinclude variable gap sizes between electrodes. For example, FIG. 7Adepicts electrode formations of 100, 150, 200 and 300 μm spacing in thechannel region. In another exemplary embodiment, a multi-layer,orthogonal pattern may be used, as depicted in FIG. 8A. In yet anotherexemplary embodiment, a concentric circle electrode pattern may be used,as depicted in FIG. 8B, such that traveling waves effectively move theparticles or cells into the circles, out of the circles, or trap them invarious portions of the circles. In yet another exemplary embodiment,the electrodes may be “wiggly”, or generally non-linear, so as tointroduce disturbance forces and torques on nearby particles or cells.These wiggly regions may be uniform, non-uniform, random and/or periodicin nature throughout the electrodes. Again, it should be appreciatedthat the shape, spacing and pattern of electrodes may vary within agiven electrode layer, and may further vary across multiple layers, suchthat any combination of shape, size, spacing and patterning may occurwith an electrode layer and across multiple layers to create the desiredmagnetic field. The electrodes may be composed of any suitableconductive material, such as copper as would be understood by thoseskilled in the art. The electrodes can be fabricated by wet etching thecopper layer of a thermal-clad printed circuit board (on an insulatedmetal substrate) through a photoresist mask. It should be appreciatedthat any type of etching or other suitable fabrication method may beused in creation of the electrodes, as would be understood by thoseskilled in the art.

The channel can include at least one inlet and at least one outlet, andmay run at an angle such that the channel ultimately transverses theelectrodes. For example, in one embodiment, the microfluidic channel canbe rotated by about 90 degrees so that the electrodes of the device aresubstantially parallel to its length. In other embodiments, the channeltransverses the electrodes at an angle between about 1-90 degrees, andany whole or partial increments therebetween. In a further exemplaryembodiment, the channel transverses the electrodes in a substantiallystraight line. In still other exemplary embodiments, the channeltransverses the electrodes in a curved, bent or generally non-linearpattern. The microfluidic channel can range from 20-100 μm, 1-3 mm wideand 2-3 cm in length, and any whole or partial increments therebetween.In other exemplary embodiments, the channel may include any number andsize of pockets, ridges, grooves, trenches, and/or slopes within thechannel walls, such that the particles or cells traveling within thechannel can be locally concentrated or dispersed, based on theconformational effects of the contours of the channel walls. Additionalexemplary channels, having multiple inlets and outlets, are depicted inFIG. 7B. The channels may be composed of any suitable material as wouldbe understood by those skilled in the art. In one embodiment, thechannel may be prepared from polydimethylsiloxane (PDMS) stamps throughsoft lithography, and bonded to an insulating layer of very thin PDMScovering the electrodes (Mao et al., 2006, Nanotechnology 17:34-47). Incertain embodiments, the channel height may be selected to be well belowthe optimum for localized ferrohydrodynamic flow, in order to minimizeits potential effects on particle migration. While not required, thechannel can be washed with a 1% triton-X solution for about 10 minutesbefore introducing the ferrofluid/microsphere mixture into themicrofluidic device, to minimize particle attachment to the PDMS walls.It should be appreciated that the substrate, insulating layer andchannel can each alternatively be composed of materials having similarfeatures and/or properties, as would be understood by those skilled inthe art. Thus, the devices of the present invention can be constructedon an inexpensive printed circuit board that features an insulatedcopper layer etched via a single, low-resolution transparency mask todefine the electrodes. The microfluidic channel can be constructed viasoft lithography using a low-resolution mold. In certain embodiments,device fabrication does not necessitate a clean room, and hence, can befabricated rapidly and inexpensively.

A travelling magnetic field may be generated within the channel from apower source by applying current to the electrodes to create a magneticfield pattern along the length of the microfluidic channel. Alternatingcurrents up to about 7 A peak to peak in amplitude and with frequenciesfrom about 10 Hz to 100 kHz, which correspond to a maximum magneticfield strength of about 90 Oe within the ferrofluid, can be applied tothe electrodes. In other exemplary embodiments, the generated magneticfield strength may range between 1-200 Oe, and any whole or partialincrements therebetween. In one example, the magnetic field is generatedby applying alternating currents in quadrature to a single layer ofelectrodes, to create a periodic magnetic field pattern that travelsalong the length of the microchannel. With this configuration, thedevice is able to create both magnetic field gradients, resulting in atime-average force on the cells or particles, and local rotation offerrofluid magnetization, which eventually results in torque on thenonmagnetic particles, as illustrated in FIG. 1B.

When the current is turned on, the cells or particles are pushed awayfrom the electrodes to the top of the channel, due at least in part tomagnetic force, where they start to rotate and roll along its length,due at least in part to magnetic torque. The device behavior can thusmimic the frequency-dependent susceptibility of the particularferrofluid used. For a given particle size, its speed may depend on thelocal force and torque values along the channel length, as illustratedin FIG. 1C. For example, at low frequencies, the force dominates,pushing the nonmagnetic microparticles up to the channel ceiling andinto the space between the electrodes. In another example, at highfrequencies, the rolling microparticles can overcome the diminishingrepulsion caused by magnetic force and move continuously along thechannel, as illustrated in FIG. 1D.

Using the aforementioned microfluidic setup, the typical magnetic forcethat can be applied on a particle several micrometers in diameter can beon the order of tens of piconewtons, which is significantly larger thanwhat is typical with optical tweeters on μm-size particles. In certainembodiments, this actuation force can be increased by applying largerexcitation currents. For example, a simple heat sink can maintain thechannel contents at room temperature up to 10-A peak-to-peak inputcurrent (Mao L, Koser H (2006) Toward ferrofluidics for μ-TAS and labon-a-chip applications. Nanotechnology 17:34-47).

Biocompatible Ferrofluids

Ferrofluids are colloidal mixtures of nanometer sized magneticparticles, such as cobaltferrite, covered by a surfactant, suspended ina carrier medium that is compatible with the surfactant material. Forexample, a sample reaction that results in magnetite particles is asfollows:

2 FeCl3+FeCl2+8 NH3+4H2O→Fe3O4+8 NH4Cl

A 10% by volume suspension of magnetite has a saturation magnetizationof around 560 G. The magnetization of each single-domain particleresponds to a high magnetic field with a time constant on the order of10 μs. High magnetic field gradients can be used to position theferrofluid. “Spikes” and other interesting features may appear at theferrofluid surface in the presence of such high fields.

In one embodiment, particle diameters can range from about 1 nm to about100 nm, and any whole or partial increments therebetween. For example,end without limitation, the particle diameters can range between 1-10nm, 1-20 nm, 5-50 nm, or 10-100 nm. In a preferred embodiment, particlediameters average about 10 nm. Volume fractions may range from 0.1% toabout 10%, and any whole or partial increments therebetween.

In another embodiment, the ferrofluids of the present invention arebiocompatible and can sustain live cells for several hours withoutdeterioration in physical properties or sustainability, allowing forextended examination of the target sample. The biocompatible ferrofluidcan be suitable for sustaining any living cell type and/or shape, suchas any animal or plant tissue cell type, any microorganism, or anycombination thereof, for example. Of course, the ferrofluid is alsosuitable for suspending any type of particle, and for any sized orshaped particle, or particle is clusters or clumps, whether living ornon-living.

Citrate is an effective surfactant in ferrofluids, and it is mostlybiocompatible in cell cultures as well. Therefore, in one embodiment,citrate was utilized both to stabilize the ferrofluid and to provide anionic medium for the cells to survive in. In this context, determining anovel and optimum citrate concentration was necessary, as too little ortoo much citrate would result in particle aggregation and precipitationwithin the ferrofluid. Further, cell survival within the ferrofluiddepends on having enough ionic species to control the osmotic pressureon the cells to promote sustainability. In one exemplary embodiment, acitrate concentration within the ferrofluid resulting in a stablecolloidal suspension of magnetic nanoparticles was about 40 mM. Whilehigher citrate concentrations might begin to gradually destabilize theferrofluid, concentrations of citrate may range anywhere between 5-200mM, and any whole or partial increments therebetween, depending on thecharacteristics and type of ferrofluid used. In the exemplary embodimentdepicted in FIG. 2C, it was also determined that the minimumconcentration of citrate, stabilized with citric acid to result in a pHof about 7.4, that first resulted in substantial cell survival over thecourse of several hours was about 40 mM. At this ionic concentration,the cells were viable and the ferrofluid was stable. Hence, in apreferred embodiment, a citrate concentration of about 40 mM can be usedas effective biocompatible ferrofluid. As contemplated herein, anddepending on the type of ferrofluid used, the ferrofluids of the presentinvention may also be stabilized at pH ranges from between about 2-11,and any whole or partial increments therebetween. In certainembodiments, the ferrofluid is biocompatible, such that cells cansurvive within the ferrofluid for at least about 1 hour, about 2 hours,about 3 hours, about 5 hours, about 10 hours, and even up to about 24hours.

Calculations for Particle Manipulation

Provided herein is an analytical approach that enables the estimation ofparticle velocities and critical frequencies observed in theferromicrofluidic devices of the present invention. To simplify thecalculations, a perfectly spherical, incompressible microparticle, amagnetically linear ferrofluid, and a slip factor (see below) that isindependent of field magnitude and frequency are assumed. Furtherassumed is that the spherical particle radius (R) is small compared tothe wavelength of the travelling magnetic field ({right arrow over(H)})—as determined by electrode dimensions and spacing, so theR|∇{right arrow over (H)}|<<|{right arrow over (H)}| holds true. Underthese assumptions, the ferrofluid magnetization in the immediatevicinity of the microparticle—and, the virtual magnetization (M_(eff))within the particle's volume (V_(p))—can be approximated as uniform. Itis also approximated that any field value (but not its gradient) isconstant within the interior extent of the microparticle

The total instantaneous force on that dipole is then given by

$\begin{matrix}{{\overset{\rightarrow}{F}}_{ins} = {\int_{V_{p}}{{\nabla\left( {{\overset{\rightarrow}{M}}_{eff} \cdot {\overset{\rightarrow}{B}}_{in}} \right)}{dV}}}} & (1)\end{matrix}$

where B_(in) is the magnetic flux density within the sphericalmicroparticle and the integration is over the internal volume of theparticle (Zahn et al., 1995, J of Magnetism and Magnetic Materials149:165-173). Under these assumptions, the surface terms in (1) due todiscontinuities in M and B create pressure terms that integrate out to0, and a simple vector expansion of the integrand reveals that this termis the same as the Kelvin force density. Hence, the instantaneous forceexpression can be simplified to

{right arrow over (F)} _(int) =V _(p)∇({right arrow over (M)} _(eff)·{right arrow over (B)} _(m))  (2)

To obtain an eventual analytical expression for the magnetic force, itis helpful to express M_(eff) and B_(in) in terms of the externalmagnetic field (H_(ext)) in the absence of the microparticle, since thisfield value can be easily obtained from simple simulations. The netmagnetization of the particle with a magnetic permeability μ_(p)(essentially μ₀) within the ferrofluid (with a complex,frequency-dependent permeability μ_(j)=μ_(o)(1+χ_(f))) depends onH_(ext) as follows

$\begin{matrix}{{\overset{\rightarrow}{M}}_{eff} = {\left. {3\left( \frac{\mu_{p} - \mu_{f}}{\mu_{p} + {2\; \mu_{f}}} \right){\overset{\rightarrow}{H}}_{ext}}\Rightarrow{\overset{\rightarrow}{M}}_{eff} \right. = {\frac{{- 3}\; \chi_{f}}{3 + {2\; \chi_{f}}}{\overset{\rightarrow}{H}}_{ext}}}} & (3)\end{matrix}$

Determining the magnetic flux density field within the particle requiresconsideration of the demagnetization field inside it. The overall fieldinside the particle is {right arrow over (H)}_(in)={right arrow over(H)}_(ext)−{right arrow over (H)}_(dmag), with {right arrow over(H)}_(dmag)={right arrow over (M)}_(eff)/3 for a sphere. Hence, in thelinear regime where particle magnetization can be written as {rightarrow over (M)}_(eff)=χ_(eff){right arrow over (H)}_(in), one finds

$\begin{matrix}{\frac{{\overset{\rightarrow}{M}}_{eff}}{\chi_{eff}} = {\left. {{\overset{\rightarrow}{H}}_{ext} - \frac{{\overset{\rightarrow}{M}}_{eff}}{3}}\Rightarrow{\overset{\rightarrow}{M}}_{eff} \right. = {\left( \frac{{3\; \chi_{eff}}\;}{3 + \chi_{eff}} \right){\overset{\rightarrow}{H}}_{ext}}}} & (4)\end{matrix}$

Comparing (3) and (4) reveals the effective susceptibility of theparticle in terms of the ferrofluid susceptibility:

$\begin{matrix}{\chi_{eff} = \frac{- \chi_{f}}{1 + \chi_{f}}} & (5)\end{matrix}$

Note that the effective magnetic susceptibility depends on that of theferrofluid, since the microparticle responds to magnetic forces onlybecause it displaces ferrofluid and creates a “magnetic hole”. In thatregard, the magnetic medium in which the hole resides determines thestrength of the interactions between that magnetic hole and appliedfields. The negative sign in (5) indicates that the effectivemagnetization of the microparticle is in the opposite direction of thelocal ferrofluid magnetization under static conditions. Whileχ_(eff)≈−χ_(f) for χ_(f)<<1, the effective susceptibility of themagnetic hole approaches −1 in a strongly magnetisable medium. Ineffect, using too strong a ferrofluid for microparticle manipulationcould be counter-productive.

The instantaneous magnetic, force on the particle can be expressed as

$\begin{matrix}\begin{matrix}{{\overset{\rightarrow}{F}}_{ins} = {{V_{p}{\nabla\left( {{\overset{\rightarrow}{M}}_{eff} \cdot {\overset{\rightarrow}{B}}_{in}} \right)}} = {B_{p}\mu_{0}{\overset{\rightarrow}{\nabla}\left( {{\overset{\rightarrow}{M}}_{eff} \cdot \left( {{\overset{\rightarrow}{H}}_{in} + {\overset{\rightarrow}{M}}_{eff}} \right)} \right)}}}} \\{= {V_{p}\mu_{0}{\overset{\rightarrow}{\nabla}\left( {{{\overset{\rightarrow}{M}}_{eff} \cdot {\overset{\rightarrow}{H}}_{in}} + {{\overset{\rightarrow}{M}}_{eff}}^{2}} \right)}}} \\{= {V_{p}\mu_{0}{\overset{\rightarrow}{\nabla}\left( {{{{\overset{\rightarrow}{M}}_{eff}}\frac{{\overset{\rightarrow}{M}}_{eff}}{\chi_{eff}}\cos \; \theta} + {{\overset{\rightarrow}{M}}_{eff}}^{2}} \right)}}} \\{= {V_{p}\mu_{0}{\overset{\rightarrow}{\nabla}\left( {{{{\overset{\rightarrow}{M}}_{eff}}^{2}\frac{{Re}\left\{ \chi_{eff} \right\}}{{\chi_{eff}}^{2}}} + {{\overset{\rightarrow}{M}}_{eff}}^{2}} \right)}}}\end{matrix} & (6)\end{matrix}$

Here, θ is the angle between {right arrow over (M)}_(eff) and {rightarrow over (H)}_(in), given by the angle of the complex susceptibilityχ_(eff). Using

${{\overset{\rightarrow}{M}}_{eff} = {3\left( \frac{- \chi_{f}}{3 + {2\; \chi_{f}}} \right){\overset{\rightarrow}{H}}_{ext}}},$

we get

$\begin{matrix}{{\overset{\rightarrow}{F}}_{ins} = {V_{p}{\mu_{0}\left( {\frac{{Re}\left\{ \chi_{eff} \right\}}{{\chi_{eff}}^{2}} + 1} \right)}\left( \frac{9{\chi_{f}}^{2}}{9 + {6\; {Re}\left\{ \chi_{f} \right\}} + {4{\chi_{f}}^{2}}} \right){\overset{\rightarrow}{\nabla}{{\overset{\rightarrow}{H}}_{ext}}^{2}}}} & (7)\end{matrix}$

In the presence of traveling fields, the local magnetic field variessinusoidally, and the time-average force is just half the maximum valueof the instantaneous force:

$\begin{matrix}{{\overset{\rightarrow}{F}}_{ave} = {\frac{1}{2}V_{p}{\mu_{0}\left( {\frac{{Re}\left\{ \chi_{eff} \right\}}{{\chi_{eff}}^{2}} + 1} \right)}\left( \frac{9{\chi_{f}}^{2}}{9 + {6\; {Re}\left\{ \chi_{f} \right\}} + {4{\chi_{f}}^{2}}} \right){\overset{\rightarrow}{\nabla}{{\overset{\rightarrow}{H}}_{ext}}^{2}}}} & (8)\end{matrix}$

Similarly, the instantaneous torque on a magnetic dilpole is given by

$\begin{matrix}\begin{matrix}{{\overset{\rightarrow}{\tau}}_{ins} = {s{\int_{V_{p}}{\left( {{\overset{\rightarrow}{M}}_{eff} \times {\overset{\rightarrow}{B}}_{in}} \right){dV}}}}} \\{= {{{sV}_{p}\left( {{\overset{\rightarrow}{M}}_{eff} \times {\overset{\rightarrow}{B}}_{in}} \right)}.}}\end{matrix} & (9)\end{matrix}$

(Zahn et al., 1995, J of Magnetism and Magnetic Materials 149:165-173).Here, the possibility that the rotation of the nonmagnetic microparticlemay be subject to a slip s between 0 and 1 has been allowed for. Thisslip factor represents the ratio of the torque that a non-magneticmicroparticle experiences in the ferro-microfluidic devices of thepresent invention to the value of the torque that would be felt by anisolated particle of the same size and effective magnetization.

The remaining details of the derivation for magnetic torque mirror thosefor magnetic force. Substituting for the magnetic flux density, oneobtains

$\begin{matrix}\begin{matrix}{{\overset{\rightarrow}{\tau}}_{ins} = {{{sV}_{p}\left( {{\overset{\rightarrow}{M}}_{eff} \times {\overset{\rightarrow}{B}}_{in}} \right)} = {{sV}_{p}{\mu_{0}\left( {{\overset{\rightarrow}{M}}_{eff} \times \left( {{\overset{\rightarrow}{H}}_{in} + {\overset{\rightarrow}{M}}_{eff}} \right)} \right)}}}} \\{= {{sV}_{p}{\mu_{0}\left( {{{\overset{\rightarrow}{M}}_{eff} \times {\overset{\rightarrow}{H}}_{in}} + {{\overset{\rightarrow}{M}}_{eff} \times {\overset{\rightarrow}{M}}_{eff}}} \right)}}}\end{matrix} & (10)\end{matrix}$

Since {right arrow over (M)}_(eff)×{right arrow over (M)}_(eff)=0 and{right arrow over (M)}_(eff)=χ_(eff){right arrow over (H)}_(in), onegets

$\begin{matrix}\begin{matrix}{{\overset{\rightarrow}{\tau}}_{ins} = {\hat{y}{sV}_{p}{\mu_{0}\left( {{\left. {\overset{\rightarrow}{M}}_{eff}||{\overset{\rightarrow}{M}}_{eff} \right.}\frac{\chi_{eff}}{{\chi_{eff}}^{2}}\sin \; \theta} \right)}}} \\{= {\hat{y}{sV}_{p}\mu_{0}\frac{{Im}\left\{ \chi_{eff} \right\}}{{\chi_{eff}}^{2}}\left( \frac{9{\chi_{f}}^{2}}{9 + {6\; {Re}\left\{ \chi_{f} \right\}} + {4{\chi_{f}}^{2}}} \right){{\overset{\rightarrow}{H}}_{ext}}^{2}}}\end{matrix} & (11)\end{matrix}$

And time average torque is given by

$\begin{matrix}{{\overset{\rightarrow}{\tau}}_{ave} = {\hat{y}\frac{V_{p}}{2}s\; \mu_{0}\frac{{Im}\left\{ \chi_{eff} \right\}}{{\chi_{eff}}^{2}}\left( \frac{9{\chi_{f}}^{2}}{9 + {6\; {Re}\left\{ \chi_{f} \right\}} + {4{\chi_{f}}^{2}}} \right){{{\overset{\rightarrow}{H}}_{ext}}^{2}.}}} & (12)\end{matrix}$

A finite element analysis program (COMSOL) was used to calculate H_(ext)for given input current amplitude using a realistic, two-dimensionalcross-section of the ferromicrofluidic channel and the electrodesunderneath. The Reynolds' number associated with the motion ofmicron-scale beads and cells in a quiescent ferrofluid is very small. Inthis regime, inertial effects can be neglected and Stokes flow equationsdominate hydrodynamics. Hence, the equilibrium between viscous drag andmagnetic forces determine microparticle dynamics. Since Stokes flowequations are linear, all hydrodynamic coefficients involved can becombined into a resistance matrix:

$\begin{matrix}{{{\left\lfloor \begin{matrix}F_{{ave},x} \\\tau_{{ave},y}\end{matrix} \right\rfloor = {A\left\lfloor \begin{matrix}v_{x} \\\omega_{y}\end{matrix} \right\rfloor}},{with}}{A = \begin{pmatrix}{6\; \pi \; \eta \; {{Rf}_{1}\left( {h,R} \right)}} & {6\; \pi \; \eta \; R^{2}{f_{2}\left( {h,R} \right)}} \\{8\; \pi \; \eta \; R^{2}{f_{3}\left( {h,R} \right)}} & {8\; \pi \; \eta \; R^{3}{f_{4}\left( {h,R} \right)}}\end{pmatrix}}} & (13)\end{matrix}$

(Happel J, Brenner H (1983) Low Reynolds Number Hydrodynamics withspecial applications to particulate media. (Martinus Nijhoff:Dordrecht)). Here, v is the linear velocity of the microparticle alongthe channel length, ω is its angular velocity, η is the ferrofluidviscosity, R is microsphere radius, and f_(i) is a resistance factorthat depends on particle radius and its distance (h) from the channelceiling. Assuming h<<R, these resistance factors can be obtained fromstandard lubrication theory as

f ₁≈− 8/15ln(h/R)+0.9588; f ₂≈− 2/15ln(h/R)−9.2526

f ₃≈− 1/10ln(h/R)−0.1895; f ₄≈−⅖ln(h/R)+0.3817.  (14)

(Goldman et al., 1967, Chem Engl Sci 22:637-651). In general, it ispossible to estimate h through Derjaguin, Landau, Verwey and Overbeektheory (DLVO theory) (Ise, 2007, Proc Jpn Acad B Phys Biol Sci83:192-198) using the surface charge density on the microparticle andthe channel surfaces, given the ionic conditions within the ferrofluid.Interestingly, the vertical force (F_(ave,y)) that pushes themicroparticles up to the channel ceiling is on the order of nN's andthey are expected to be close to touching the channel wall.

Equation (13) can be solved for v and ω through a simple matrixinversion,

$\begin{matrix}{{\left\lfloor \begin{matrix}v_{x} \\\omega_{y}\end{matrix} \right\rfloor = {A^{- 1}\left\lfloor \begin{matrix}F_{{ave},x} \\\tau_{{ave},y}\end{matrix} \right\rfloor}}{where}{A^{- 1} = \frac{\begin{pmatrix}{8\; \pi \; \eta \; R^{3}{f_{4}\left( {h,R} \right)}} & {{- 6}\; \pi \; \eta \; R^{2}{f_{2}\left( {h,R} \right)}} \\{{- 8}\; \pi \; \eta \; R^{2}{f_{3}\left( {h,R} \right)}} & {6\; \pi \; \eta \; {{Rf}_{1}\left( {h,R} \right)}}\end{pmatrix}}{48\; \pi^{2}\eta^{2}R^{4}G}}} & (15)\end{matrix}$

Here G=f₁f₄−f₂f₃ has been defined for notational convenience. Hence,particle linear velocities due to magnetic three and torque alone can bedetermined:

$\begin{matrix}{v_{{force},x} = {\frac{f_{4}}{6\; \pi \; \eta \; {RG}}F_{{ave},x}}} & (16) \\{v_{{torque},x} = {{- \frac{{sf}_{2}}{8\; \pi \; \eta \; R^{2}G}}{\tau_{{ave},y}.}}} & (17)\end{matrix}$

Net particle, velocity is then given by

v _(x) =v _(force,x) +v _(torque,x′)  (18)

Both magnetic force and torque scale with particle volume (R¹); from(16) and (17), it is clear that particle velocity due to magnetic forcedepends on R², whereas that due to torque scales with R. Thisobservation indicates that torque effects on smaller particles isrelatively more significant; and explains why smaller microparticlesdisplay smaller critical frequencies in their dynamics.

The preceding theoretical approach explains the experimental resultsvery well (e.g., FIG. 4A) for a slip factor of 1 and h of about 1 nm,confirming the expectation that the microparticles are indeed pushedstrongly towards the channel ceiling. The slip factor of 1 implies thatthe microspheres rotate under no-slip conditions.

Force on a Magnetic Dipole

In general the magnetic force on a magnetic dipole can be found usingthe Kelvin force expression, i.e.,

$\begin{matrix}{\overset{\rightarrow}{F} = {\mu_{0}{\int_{V_{P}}{\left( {\overset{\rightarrow}{M} \cdot \nabla} \right)\overset{\rightarrow}{H}{dV}}}}} & (19)\end{matrix}$

This expression h approximately equivalent to equation (1).

A key assumption is that the applied field is not too inhomogeneous andthe particle radius (R) is small enough, such at R|∇{right arrow over(H)}|<<|{right arrow over (H)}| in any direction. Under this assumption,the magnetization of the ferrofluid immediately surrounding themicroparticle can be taken as uniform. It is further approximated thatany field value (but not its gradient) is constant within the interiorextent of the microparticle.

With these simplifying assumptions in mind, vector identities can beused to rewrite the integrand of (1) as follows:

∇({right arrow over (M)}·{right arrow over (B)})={right arrow over(M)}×(∇×{right arrow over (B)})+{right arrow over (B)}×(∇×{right arrowover (M)})+({right arrow over (M)}·∇){right arrow over (B)}+({rightarrow over (B)}·∇){right arrow over (M)}.  (20)

The first term on the right-hand-side (RHS) of (20) involves the curl ofthe magnetic flux density, which could be expanded as

{right arrow over (M)}×(∇×{right arrow over (B)})={right arrow over(M)}×(∇×{right arrow over (H)})+{right arrow over (M)}×(∇×{right arrowover (M)})  (21)

The curl of the magnetic field is 0 everywhere within the integrationvolume of (1), since both the ferrofluid and the plastic microparticleare insulating and do not support electrical currents. Hence, the firstterm on the RHS of (21) vanishes. The curl of the magnetization is 0inside the microparticle, but across its surface, the effectivemagnetization changes as a step. Therefore, surface contributions to theforce density should, in general, be considered. However, since themagnetization of the ferrofluid immediately surrounding themicroparticle is assumed to be constant, the second term of (21) alsovanishes when integrated around a sphere (due to symmetry). The samelogic could be applied to the {right arrow over (B)}×(∇×{right arrowover (M)}) term in (20): (∇×{right arrow over (M)}) is 0 inside themicrosphere and {right arrow over (B)}×(∇×{right arrow over (M)})integrates to 0 around the sphere surface with the magnetic flux densityand ferrofluid magnetization assumed constant in the immediate vicinityof the microsphere.

With the same reasoning, the ({right arrow over (B)}·∇){right arrow over(M)} term to (20) will also be 0 inside the microsphere and integrate to0 around it. The only term that involves the non-zero gradient of afield vector then is

$\begin{matrix}{\overset{\rightarrow}{F} = {\int_{V_{P}}{\left( {\overset{\rightarrow}{M} \cdot \nabla} \right)\overset{\rightarrow}{B}{{dV}.}}}} & (22)\end{matrix}$

The integral is valid over the volume of the microparticle, which isnonmagnetic. Hence, inside the nanoparticle, {right arrow over(B)}=μ₀{right arrow over (H)} and (22) becomes the same as (19). Inother words, under the assumptions outlined above, (1) and (19) areequivalent in the case of the setup presented herein.

The equation in (1) is preferably used as the force expression insteadof that in (19), since the former leads to a force whose direction isdetermined by the gradient operator—requiring taking a single derivativealong a given spatial direction to determine the force along thatdirection.

Also considered is what happens to surface gradients associated with theexpression in (1). Once again, using the assumption that the ferrofluidmagnetization and the magnetic flux density are constant inside and justaround the microsphere surface (but not their derivatives), it can bedetermined that

$\begin{matrix}{F_{x} = {{\int_{V_{p}}{\frac{\partial}{\partial x}\left( {\overset{\rightarrow}{M} \cdot \overset{\rightarrow}{B}} \right){dV}}} = {\int_{V_{p}}{\frac{\partial}{\partial x}\left( {M_{x}{B_{x} \cdot M_{z}}B_{z}} \right){dV}}}}} & (23)\end{matrix}$

Here, the field and magnetization vectors are taken to be in the x-zplane due to the symmetry of the ferro-microfluid channel. In theprevious section, the expression in (23) is evaluated only within theinterior of the microparticle to calculate the x-directed force. Now,without any loss of generality, the microsphere center is taken as theorigin. Both {right arrow over (M)} and {right arrow over (B)} arediscontinuous at the particle-ferrofluid boundary, so their derivativesresult in an impulse; when integrated across the microsphere surface,each contribution M_(x,out)B_(x,out)−M_(z,in)B_(z,in) to the integralfrom a surface patch at x=√{square root over (R²−y²−z²)} gets cancelledout by the negative of that contribution at the opposite patch atx=−√{square root over (R²−y²−z²)}. The resulting surface integral is 0.By spherical symmetry, the same is true for the terms in F₂. Hence,under the described assumptions, evaluating equation (1) within theinterior of the microparticle yields the magnetic force on it.

System and Methods of Separation

The present invention also relates to a flow-based assay systemincorporating the aforementioned biocompatible ferrofluids. In oneembodiment, a much higher throughput can be achieved by conducting thebioferrofluidic separation while fluid flow continuously introducesfresh cells into the inlet of the channel. At the outlet, the incomingbeads or cells are sorted into different output channels. From there,the cells can be collected for inspection or directed towards anexternal or internal (i.e., integrated) sensor. For example, the flowdevice allows a sample suspended within the ferrofluid to enter thedevice inlet and pass through the separation chamber, and exit viamultiple outlets designed for capturing particles of a particular size.For example, as depicted in FIG. 9, 2 μm particles can flow to outlet A,5 μm particles flow to outlet B, etc., and the remaining sample flows toa waste outlet C. In certain embodiments, flow is not needed to directcells. Instead, magnetic excitation can be used to direct them. Further,the sensor may be directly integrated into a side pocket along the flowchannel, for example.

Manipulation is not only dependent on cell size, but also on the shapeand elasticity of the cells. For example, the variable size, shape andelasticity of bacteria and sickle cells allows them to be separated fromhealthy blood cells. According to an aspect of the present invention,particle separation can be dependent on size and frequency. In anotherembodiment, critical frequency, as described hereinthroughout, may alsodepend on the electrode gap. For example, larger microspheres can betrapped first in smaller gaps. By utilizing this phenomenon, sorting canbe performed based on particle or target size. Further, the system mayalternate between the manipulation excitation at the chosen frequencyand another frequency that helps break possible nanoparticle chains thatmay form due to the magnetic excitation. According to an aspect of thepresent invention, “wiggly” electrodes can be used to prevent beads orcells from clustering into large chunks as they flow down the channel.The “wiggly” electrodes introduce disturbance forces and torques on thebeads or cells to break clusters apart, allowing for larger individualbeads or cells to line up like pearls on a necklace. By periodicallybreaking the nanoparticle chains, the ferrofluid physical properties arekept constant over time. Further, target cells can be concentrated,trapped, localized, or simply directed toward sensor surfacesefficiently, rapidly, and in a label-free fashion. For example, themethod of separation can direct a cell or particle type based on size,shape or elasticity into an outlet, or by trapping a cell or particletype based on size, shape or elasticity via increasing or decreasing thespacing between electrodes.

Thus, the present invention includes a method for separating at leastone cell type from a sample. The method includes the steps of suspendingcells in a biocompatible ferrofluid to form a sample, passing the samplethrough a microfluidic channel that transverses a plurality ofelectrodes at about 90% such that the plurality of electrodes aresubstantially parallel to the length of the microfluidic channel,applying a current to the plurality of electrodes to create a magneticfield pattern along the length of the microfluidic channel, and sortingthe cells into at least one output channel based on a variation of atleast one of cell size, shape and elasticity. Separation can occur viaconcentrating, trapping, localizing, or simply directing toward sensorsurfaces efficiently, rapidly, and in a label-free fashion.

The present invention also provides for a method for separating cellsand/or particles based on side. This size-based separation can bedemonstrated with about 50% efficiency, about 60% efficiency, about 70%efficiency, about 80% efficiency, about 905 efficiency, about 92%efficiency, about 94% efficiency, about 96% efficiency, about 97%efficiency, about 98% efficiency and about separation efficiency. Sizerevolution in the separation process can be less than shout 10 μm, lessthan about 9 μm, less than about 8 μm, less than about 7 μm, less thanabout 6 μm, less than about 5 μm, less than about 4 μm, less than about3 μm, less than about 2 μm, less than about 1 μm, less than about 0.5μm, less than about 0.1 μm, and less than about 10 nm. Such separationcan be accomplished in less than about 2 m, less than about 1 m, lessthan about 45 s, less than about 30 sec, less than a hour 20 s, and lessthan about 10 s.

The present invention also provides for the continuous manipulation andshape-based separation of cells, such as live red blood cells fromsickle cells and/or bacteria. These demonstrations highlight the abilityof ferromicrofluidics to significantly reduce incubation limes andincrease diagnostic sensitivity In cellular assays through rapidseparation and delivery of target cells to sensor arrays.

The microfluidic system of the present invention has a number of uniqueadvantages, in that it provides a laminar flow platform for use withtiny sample sizes. The system further provides fast diffusion and fastresults, can be portable, and can be integrated with other existingsensors. For example, the present invention can be used for thesterilization of adult stem cells obtained from blood samples, for usein the context of wound healing and organ regeneration for soldiers andmarines in combat. The present invention can also be used for the rapiddetection (i.e., <1 min) of low-level bacterial contamination in donatedblood. This can be particularly useful in battlefield trauma emergencysituations. The present invention can also be utilized for“needle-in-haystack” applications that require the detection ofultra-low concentrations of cells in blood, such as searching forcirculating tumor cells in blood.

EXPERIMENTAL EXAMPLES

The invention is now described with reference to the following Examples.These Examples are provided for the purpose of illustration only and theinvention should in no way be construed as being limited to theseExamples, but rather should be construed to encompass any and allvariations which become evident as a result of the teaching providedherein.

Without further description, it is believed that one of ordinary skillin the art can, using the preceding description and the followingillustrative examples, make and utilize the present invention andpractice the claimed methods. The following working examples therefore,specifically point out the preferred embodiments of the presentinvention, and are not to be construed as limiting in any way theremainder of the disclosure.

Ferrofluid Preparation

A co-precipitation method was used to synthesize cobalt-ferritenanoparticles that were eventually incorporated into a water-basedferrofluid with a 20% solid content (Khalafalla S E, Reimers G W (1973)U.S. Pat. No. 3,764,540). Cobalt-ferrite nanoparticles were precipitatedout of a boiling solution of 1 M sodium hydroxide by adding a mixture ofcobalt (II)-chloride hexahydrate and iron (III)-chloride. The magneticprecipitate was washed twice using DI water. 2 M nitric acid and a 0.35M solution of iron (III)-nitrate were added to the precipitate (Massart,1981, IEEE Trans Magn 17:1247-1248; Fischer et al., 2008, IEEE Int Confon Nano/Micro Eng and Molecular Syst China, 907-910). This mixture wasthen stirred at 80° C. for 20 minutes. The nitric acid solution was thendecanted while the precipitate was held in place with a magnet.Cobalt-ferrite particles within the precipitate were later dispersed inDI water, and the resulting ferrofluid was dialyzed for one week againsta 40 mM sodium citrate and citric acid sedation at a pH level of 7.4.The solution was refreshed on a daily basis during dialysis. Theresulting ferrofluid had a viscosity of 1.5 cP at 20° C.

TEM Sample Preparation

The TEM Images were using a Tecnai 12 electron microscope from Philips(120 keV). A copper/rhodium grid (from Electron Microscopy Sciences) wascovered with a thin carbon film and dipped into a ferrofluid samplediluted with ethanol. After TEM images were obtained, particle sizes inthe images were characterized using imageJ software(http://rsbweb.nih.gov/ij/). The distribution of magnetic nanoparticlecore sizes, as obtained from the TEM images (around 200 particlescounted), was fitted with a lognormal probability density function as

$\begin{matrix}{{F(D)} = {\frac{1}{\sqrt{2\; \pi}D\; \sigma}{\exp \left( {- \frac{\left( {{\ln \; D} - {\ln \; D_{0}}} \right)^{2}}{2\; \sigma^{2}}} \right)}}} & (24)\end{matrix}$

where D is the random variable depicting core diameter, while D₀ and σare the mean and standard deviation of ln(D), respectively.

AC Susceptibility Measurements

The frequency-dependent AC susceptibility of the ferrofluid can beobtained by measuring the changes in the mutual inductance of anelectromagnetic coil pair, with and without the presence of a ferrofluid(Maiorov, 1979, Magnetohydrodynamics 15:135-139). In this regard, apick-up coil (of 200 turns, with an average diameter of 9.76 mm) wascentered within a solenoidal excitation coil (of 340 turns with anaverage diameter of 13.34 mm), and the mutual inductance of the twocoils was characterized via an LCR meter for Agilent (E4980A). Theferrofluid sample was introduced within the two sets of coils in a 1 ccplastic syringe. The symmetry in the setup ensured parallel field linesat the location of the pick-up coil and enabled an analyticalcalculation of mutual inductance, and eventually, AC susceptiblity, frommeasured data.

The magnetization relaxation equation, assuming no fluid motion orconvection (Rosensweig R E (1997) Ferrohydrodynamics (Dover: N.Y.)), is

$\begin{matrix}{{\frac{d\; \overset{\rightarrow}{M}}{dt} - {\omega \times \overset{\rightarrow}{M}}} = {{- \frac{1}{\tau}}\left( {\overset{\rightarrow}{M} - {\chi_{0}\overset{\rightarrow}{H}}} \right)}} & (25)\end{matrix}$

where ω is the local vorticity within the ferrofluid, χ₀ is the DCsusceptibility value of the ferrofluid, and τ is the magnetic relaxationtime constant associated with the magnetic nanoparticles. The uniformmagnetic field within the cylindrical setup leads to a symmetry thatmakes vorticity (and hence, the second term an (25)) negligible withinthe measurement volume. The magnetic relaxation time constant representsa combination of two physical relaxation processes. If the magneticcores of the particles are small enough, their magnetic moment willsimply rotate inside the nanoparticles (Néel relaxation) (Rosensweig R E(1997) Ferrohydrodynamics (Dover: N.Y.)) with a characteristic timeconstant given by

$\begin{matrix}{\tau_{N} = {\frac{1}{f_{0}}e^{({K_{a}{V/k_{B}}T})}}} & (26)\end{matrix}$

where f₀ is a precession frequency (typically in the range 10⁸-10¹² Hz),K_(a) is a magnetic anistropy energy density, V_(core) is the magneticcore volume of the nanoparticle, and k_(B)T is the thermal energy.Particles with larger cores will have higher magnetic anisotropyenergies, leading to fixed magnetic moments within the cores, and theparticles themselves will rotate in solution to orient with the appliedfield (Brownian relaxation) with a characteristic time constant given by

$\begin{matrix}{\tau_{B} = {\frac{\pi \; D_{hyd}^{3}}{2\; k_{B}T}\eta}} & (27)\end{matrix}$

Here, η the dynamic viscosity of the fluid, k_(B) is the Boltzmann'sconstant, T is the absolute temperature (in Kelvins), and D_(hyd) is thehydrodynamic diameter of the particle, including its surfactant layer.The faster of the two mechanisms dominates the relaxation process.Cobalt-ferrite possesses a high magnetic anisotropy energy density(between 1.8×10⁵ and 3.0×10⁵ J/m³ for bulk material and up to 3.15×10⁶J/m³ for nanoparticles (Tung et al., 2003, J Appl Phys 93:7486-7488)),and ferrofluids based on this material relax primarily by particlerotation (Brownian mechanism) above a critical nanoparticle size ofabout 5 nm in diameter. Since most of the nanoparticles observed in theTEM pictures were larger than this critical size, only the Brownian timeconstant was considered in interpreting our AC susceptibilitymeasurements.

The sinusoidal steady-state solution to (25) in the absence of vorticityyields the concept of an effective susceptibility that describes themagnitude and phase relationship between ferrofluid magnetization andthe applied field as a function of frequency f:

$\begin{matrix}{{\chi (f)} = {\frac{\chi_{0}}{\left( {1 + {i\; 2\; \pi \; f\; \tau}} \right)} = {\frac{\chi_{0}}{\left( {1 + \left( {2\; \pi \; f\; \tau} \right)^{2}} \right)} - {i\frac{2\; \pi \; f\; \tau \; \chi_{0}}{\left( {1 + \left( {2\; \pi \; f\; \tau} \right)^{2}} \right)}}}}} & (28)\end{matrix}$

(Debye P J W (1929) Polar Molecules. (Dover: N.Y)) Here, χ₀ is the DCsusceptibility value of the ferrofluid and τ is the Brownian relaxationtime constant associated with the magnetic nanoparticles.

Ferrofluids consist of particles with a size distribution (typicallylognormal), which leads to a distribution of the relaxation times aswell. To take this into account, we describe the overall ACsusceptibility as a linear combination of all susceptibility spectrathat would result from the particle sizes present in the ferrofluid,weighed by the lognormal probability density function F(D_(hyd))associated with a given particle size:

$\begin{matrix}{{\chi (f)} = {\frac{1}{A}{\int_{0}^{\infty}{\frac{\chi_{0}}{\left( {1 + {i\left( {2\; \pi \; f\; \tau_{B}} \right)}} \right)}V_{core}^{2}{F\left( D_{hyd} \right)}{dD}_{hyd}}}}} & (29)\end{matrix}$

The magnitude of the total magnetization within a nanoparticle isproportional to its core volume; so is its individual contribution tothe susceptibility spectrum. Hence, the probability density function in(24) is scaled by V_(core) ². The normalization factor A is given by

$\begin{matrix}{A = {\int_{0}^{\infty}{{F\left( D_{hyd} \right)}V_{core}^{2}{dD}_{hyd}}}} & (30)\end{matrix}$

The AC susceptibility data (FIG. 2B) can be fit with the sinusoidalsteady-state solution to the magnetic relaxation equation assuming alog-normal distribution of hydrodynamic diameters (equations (27)through (30)). Simultaneously, the relative shape of the DCmagnetization data (as depicted in FIG. 2B-inset) can be fit with theLangevin equation, once again assuming the same log-normal distributionof hydrodynamic diameters (and particle concentration as a freeparameter). The simultaneous fits explain the experimental results verywell, yielding an average hydrodynamic diameter of 72.5 nm. This valueis much larger than the average core diameter of the nanoparticles asobtained with TEM. A reasonable explanation for this discrepancy isthat, in equilibrium, the nanoparticles have formed moderate-sizedaggregates that respond as single units to the magnetic fields that wereapplied during measurements. Dynamic light scattering experiments werealso conducted on diluted samples of the same ferrofluid. Those resultsconfirmed that the hydrodynamic diameters were much larger than the corediameters, supporting the explanation presented herein.

Typically, the surfactant concentration used is high enough to preventcontinuous degradation in colloidal stability (at least over severalmonths). Therefore, it is likely that the particle aggregates may haveformed during one of the brief precipitation stages of the ferrofluidsynthesis protocol, which often involves the use of a permanent magnetto speed the process. The surfactant is added later, and cannot breakaggregates that have already formed.

Dynamic Light Scattering

The dynamic light scattering experiments were conducted using a ZetaPALSinstrument from Brookhaven Instruments Group. For these measurements,the ferrofluid was diluted with DI water to avoid multiple scattering.The hydrodynamic particle diameter was found to be 64.9 nm.

Device Fabrication

The particle manipulation devise (FIG. 1A) used in the experimentspresented herein consists of two parts: the microfluid channel and theunderlying copper electrodes. The electrodes (30 μm high, 300 μm wideand 2 cm in length) were fabricated by wet etching the copper layer of athermal-clad printed circuit board (on an insulated metal substrate)through a photoresist mask. A travelling magnetic field was generated inthe channel by applying alternating currents in quadrature to a singlelayer of electrodes. The microfluidic channel (20 μm to 100 μm high, 1mm to 3 mm wide and 2 cm to 3 cm long) was prepared frompolydimethylsiloxane (PDMS) stamps through soft lithography and wasbonded to an insulating layer of very thin PDMS covering the electrodes(Mao et al., 2006, Nanotechnology 17:34-47). The channel height waschosen to be well below the optimum for localized ferrohydrodynamic flowin order to minimize its potential effects on particle migration. Inseparate experiments with sub-micron tracer particles, no discerniblehydrodynamic flow was observed. The insulated metal substrate allowsefficient heat sinking, enabling AC currents up to 10 A at low voltagesthrough the electrodes. Before introducing the ferrofluid/microspheremixture into the microfluidic device, the channel was washed with a 1%triton-X solution for about 10 minutes in order to minimize particleattachment to the PDMS walls.

Microspheres

Different sizes (1.2 μm, 1.9 μm, 2.2 μm, 3.1 μm, 5.0 μm, 6.0 μm, 9.9 μmin diameter) of green fluorescent polystyrene microspheres were obtainedfrom Duke Scientific (Fremont, Calif., USA). The coefficient ofvariation on the microsphere diameters was about 1%. These customproduced microspheres had a very low porosity and carried a minimalamount of charged groups on their surfaces. Microspheres were suspendedin deionized (DI) wafer and kept at 4° C. until they were used inferrofluid experiments.

PKH Cell Staining

To make the cells visible within the ferrofluid, blood cells werestained with green fluorescent membrane dye PKH67 (obtained fromSigma-Aldrich). This dye has an excitation peak at 490 nm and emissionat 502 nm (Horan et al., 1989, Nature 340:167-168). Cell staining wasperformed by following the manufacturer's protocol with somemodifications for our study.

General Preparation Protocol

Blood was drawn from donors prior to the experiments and kept at 4° C.prior to staining. Approximately 10 million cells were centrifuged andthe plasma was subsequently removed. The cells were then suspended in500 μl RPMI 1640 culture medium without serum (obtained from Invitrogen,Carlsbad, Calif., USA) and mixed well to remove any adherent and boundcells. The resulting suspension of cells was centrifuged again for 5minutes at 1000 rpm.

The supernatant was carefully aspirated and the pellet was suspended in500 μl Diluent C (supplied with the staining kit). Immediately afterthis, 4 micromolar PKH67 dye in Diluent C was prepared. Equal volumes ofdye and cell solutions were mixed. The resulting cell suspension wasincubated for 4 minutes, avoiding exposure to light. The stainingreaction was stopped by adding an equal volume of fetal bovine serum(FBS) and the cell suspension was further incubated for 1 minute. Thecells were then centrifuged for 5 minutes at 1200 rpm to remove thestaining solution. They were washed three times in cell culturecontaining 10% FBS to remove any remaining dye in the solution. Afterwashing was complete, the cells were suspended in culture medium. Thebrightness of labelled cells was tested with fluorescence microscopy.Before mixing with ferrofluid, the stained cells were washed withDulbecco's phosphate buffered saline (PBS) buffer containing 10% FBS.

Cell Viability Test and Cell Counting

Citrate is an effective surfactant in ferrofluids, and it is mostlybiocompatible in cell cultures as well. Therefore, citrate was utilizedboth to stabilize the ferrofluid and to provide an ionic medium for thecells to survive in. In this context, determining a novel and optimumcitrate concentration was necessary, as too little or too much citratewould result in particle aggregation and precipitation within theferrofluid. Further, cell survival within the ferrofluid depends onhaving enough ionic species to control the osmotic pressure on the cellsto promote sustainability.

The highest citrate concentration within the ferrofluid that stillresulted in a stable colloidal suspension of magnetic nanoparticles wasdetermined to the about 40 mM. Higher citrate concentrations would beginto gradually destabilize the ferrofluid.

Cell viability was monitored using the Trypan Blue (obtained fromInvitrogen) staining technique. Trypan Blue is a dye that selectivelystains dead cells blue, allowing live and dead cells to be distinguished(The Sigma-Aldrich Handbook of Stains, Dyes & Indicators, Green, F. J.,ed., Aldrich (Chemical Co. (Milwaukee, Wis.: 1990), 721-722). Followingthe manufacturer's protocol; 90 μl of 0.4% Trypan Blue Stain was addedto 10 μl of the cell suspension with a concentration of 5×10⁵ cells per1 ml of culture medium. After incubation for 5 minutes at roomtemperature, a small sample from the mixture was placed onto ahemocytometer to count live cells. It was determined that the minimumconcentration of citrate (stabilized with citric acid to result in a pHof 7.4) that first resulted in substantial cell survival over the courseof several hours was 40 mM (FIG. 2C). At this ionic concentration, thecells were viable and the ferrofluid was stable. Hence, in allexperiments involving cells suspended within our ferrofluid, a citrateconcentration of 40 mM was used.

EXAMPLE 1 Ferrofluid Properties and Device Characterization

Using highly concentrated ferrofluids with live cells has traditionallyproven to be a challenge, because it requires a carefully engineeredcolloidal system. The ferrofluid parameters that are most relevant tosustaining live cells include pH, ionic strength, andnanoparticle-surfactant combination. together with their overall andrelative concentrations. Finding the right nanoparticle-surfactantcombination is crucial in this regard: the ferrofluid needs to be stableat a pH of 7.4, and colloidal stability has to be maintained up to anionic strength that can sustain live cells. One also needs to payspecial attention to the size distribution of the nanoparticles withinthe ferrofluid. If there exist nanoparticles only a few nanometers indiameter, they could pass through the cell membrane and cause directcytotoxicity (Scherer et al., 2005, Brazilian J Phys 45:718-727). Forthis reason, the present invention includes a magnetic precipitationstep in the synthesis of the biocompatible ferrofluids to specificallyleave the smallest nanoparticles behind.

Traditional approaches to improving ferrofluid biocompatibilitytypically involve covering the magnetic nanoparticles permanently with athick polymer layer, such as dextran (Bautista, et al., 2004,Nanotechnology 15:S154-S159), because the surfactant molecules reducetoxicity by impeding direct contact with the surface of the inorganicnanoparticles. However, such an approach leads to a significantreduction in the volume content of the magnetic nanoparticles within theferrofluid, and a corresponding decline in its susceptibility. Higherferrofluid susceptibility typically translates to faster particlemanipulation, so the ferrofluid of the present invention has beenoptimized by using a short surfactant molecule.

In one embodiment, the ferrofluid of the present invention comprisescobaltferrite nanoparticles suspended in water and stabilized withcitrate. Mean nanoparticle core diameter within the ferrofluid, asdetermined with transmission electron microscopy (TEM), was found to beabout 11.3±4.4 nm (FIG. 2A). From simultaneous fits to ac susceptibilityand dc magnetization data (FIG. 2B), the average hydrodynamic diameterwas determined to be about 72.5 nm. The discrepancy between the averagehydrodynamic diameter and the individual core sizes observed in TEMimages points to a certain degree of particle aggregation within thecolloidal suspension of the ferrofluid. This finding was also continuedthrough dynamic light energy measurements, which yielded an averagehydrodynamic diameter of about 64.9 nm on highly diluted samplesferrofluid. Nevertheless, compared with the μm-sized microspheres andcells, the magnetic nanoparticles were still small enough to approximatethe ferrofluid as a continuous magnetic medium.

During synthesis, it was determined that the optimum ionic concentrationwithin the ferrofluid to provide a good compromise between cellviability (as determined by the trypan blue test) and ferrofluidstability was about 40 mM (FIG. 2C). During the course of a givenexperiment, cells retained then viability. We observed that 75% of cellsremained viable, even after being suspended in the ferrofluid forseveral hours, enabling extended tests involving live cell manipulationand separation.

Before the cell manipulation experiments, the ferromicrofluidic deviceswere characterized by using fluorescent polystyrene microspheres (DukeScientific; monodisperse sets with diameters ranging from 1.2 to 9.9μm). To understand the influence of excitation frequency and currentamplitude on the behavior of nonmagnetic nanoparticles dispersed inferrofluid, a series of experiments were performed using different sizesof microspheres at various excitation frequencies and currentamplitudes. Microspheres of a given size were mixed with the ferrofluidin small quantities (up to 1.1×10⁶ microspheres per mL for the smallestmicroparticle diameter) and subsequently added to the microfluidicchannel. The channel inlet and outlet were clamped at both ends toprevent transient fluid motion. Microspheres near the roof of themicrochannel were imaged from above with an upright fluorescentmicroscope (Zeiss Axiolmager A1) and a high-sensitivity video camera(Retiga 2000R) using StreamPix software. Image analysis was performedoffline in MATLAB (MathWorks) via an optical flow algorithm. The programcould automatically track the trajectory and determine the size ofthousands of individual microspheres within the field of view in <1 min.

During these experiments, two types of particle dynamics were observed.At low frequencies, the microspheres localized between the electrodes,where repulsive forces caused by magnetic field gradients form localminima (FIG. 3A). Frequencies above a critical value, f_(c), led tocontinuous translation of the microspheres along the length of thechannel roof; this critical frequency depended only on particle size andelectrode spacing, not on input current amplitude (FIG. 3B). The averagevelocity of microspheres of a given size depended on the excitationfrequency, current amplitude, and their location with respect to theunderlying electrodes.

In experiments with various microsphere diameters, a monotonic increasewas found in critical frequency with increasing particle size (FIG. 4A),demonstrating the potential for size-based particle separation throughexcitation frequency control. This phenomenon may be explained through asimple hydrodynamic reasoning. Both magnetic force and torque scale withparticle volume (R³); the hydrodynamic drag that resists linear particlemotion scales with R against force and R² against torque that rolls theparticle. Hence, linear particle velocity caused by magnetic force alonedepends on R², whereas that caused by torque scales with R. Thisobservation indicates that torque effects on smaller particles arerelatively more significant and explains why smaller microparticles canovercome the repulsion of magnetic force traps and propagatecontinuously within the channel at lower frequencies. The solid curvedepicted in FIG. 4A represents simulation results for critical frequencyand explains the data very well for an average microsphere-wall gap of≈1 nm and no-slip conditions applied to the rotation of themicrospheres.

FIG. 4B shows the average velocity of 2,2- and 9,9-μm microspheres(mixed in an 8:1 ratio within the same ferrofluid) under excitationfrequencies ranging from 10 Hz to 100 kHz. For a wide frequency range,the smaller particles translated continuously, whereas the largerparticles were trapped between the electrodes. In this particularexperiment and others, a mixture of particles/cells was eventuallyseparated into two groups, e.g., those trapped vs. those cleared fromchannel. Assuming that the target particle-cells are those that areintended for trapping, the trapping efficiency can be defined as theratio of the number of target moieties within the trapped group to theircorresponding number in the initial mixture. Similarly, separationefficiency is defined as the ratio of the number of nontarget moietieswithin the cleared group to their corresponding number in the initialmixture. However, particle/cell purity is simply the ratio of the numberof target cells within the trapped group to the total number of cells inthat group. At an excitation frequency of 400 Hz, 96.5% of the 9.9 μmmicrospheres (167 of 173) were trapped within 10 s, whereas the 2,2-μmparticles (1,285 of 1,294) continued to translate along the channel andwere cleared out of the observation window (45 s) without being trapped(FIGS. 4C and 4D) with a 99.3% separation efficiency. The particlepurity in the trapped group was 94.9% (167 targets of 176 total trappedparticles). Most of the small microspheres that failed to clear thechannel were stuck on the polydimethylsiloxane (PDMS) wall in randomlocations, instead of being trapped between the electrodes. With betterchannel preparation, the separation efficiency and particle purity canbe even higher.

Particle motion was also determined to depend on electrode spacing, witha smaller spacing leading to faster microsphere travel and a reductionin critical frequency (FIG. 6B). This phenomenon may be used in a devicefeaturing regions of electrodes with different gaps to use the sameexcitation frequency to separate particle mixtures with more than twodistinct sizes. One could also create an electrode pattern with agradually increasing gap to sort particles based on size (FIG. 6C). Inthis context, it was observed that small nonuniformities in actualelectrode spacing (caused by fabrication) partly determined theresolution of separation, defined as the minimum size difference inparticles that can still be separated with high efficiency (e.g., >90%).Given a range of particle sizes, this resolution of separation isdirectly related to the difference in the corresponding criticalfrequencies; under ideal conditions (i.e., perfectly controlledelectrode gaps and a very dilute cell concentration), the resolution ofseparation could be arbitrarily small. However, critical frequenciestend to show slight local variations around each nonuniform electrodegap. As depicted in FIG. 4A, the ideal critical frequency dependsnonlinearly on the particle radius; hence, a 1-μm difference in diameterbetween 9- and 10-μm microspheres is easier to resolve (with slightrandom variations in electrode spacing) than one between 1- and 2-μmparticles. Ultimately the resolution of separation that was achieved inthe experiments presented herein was ≈1 μm for particles 2 μm or larger.

EXAMPLE 2 Effects of Current Amplitude on Microparticle Speed

In additional experiments, the dependence of microparticle manipulationspeed as a function of input current amplitude was determined. Accordingto the calculations outlined in herein, and assuming the ferrofluidremains magnetically linear, the particle speed scales with the squareof the input current. As illustrated in FIG. 6A, this assumption beginsto break above 7 A peak-to-peak input current amplitude.

Electrode spacing was also varied (with electrode width fixed at 210 μm)to determine its effect on particle manipulation. A smaller electrodespacing resulted in faster average particle speeds and lower criticalfrequencies (FIG. 6B). This observation could be explained by notingthat electrodes spaced closer reduce the local magnetic field gradientthat produces the magnetic force on the microparticles; closerelectrodes also pack more energy into the fundamental of the travellingwave that produces the magnetic torque on these microparticles. A lowermagnetic force and a higher torque result in faster microparticlerotation and overall travel speed; they also result in the criticalfrequency being lowered (Tung L D, et al. (2003) Magnetic properties ofultrafine cobalt ferrite particles. J Appl Phys 93:7486-7488). Thisobservation supports the present invention for use as a microparticlesorting device in which the spacing between the electrodes could begradually increased to trap increasingly smaller particles or cells(FIG. 6C).

EXAMPLE 3 Separation of Live Cells

With the physical behavior of the ferromicrofluidic platformcharacterized, manipulation and separation experiments were conductedwith live human red blood cells and bacteria to demonstrate the utilityand practicality of the ferromicrofluidic devices of the presentinvention for biomedical applications. Red blood cells and Escherichiacoli bacteria [K 12 strain (Blattner et al., 1997, Science277:1453-1474)] were stained with a green fluorescent marker and mixedbefore suspension in ferrofluid. The average velocity for cells andbacteria within the channel was measured with 6 A of peak-to-peakcurrent amplitude for frequencies from 10 Hz to 100 kHz. The criticalfrequencies for cells and bacteria were found to be 215 and 77 Hz,respectively. These f_(c) values are somewhat lower than those found forcomparably sized polystyrene microspheres, likely due to a combinationof compliant shapes and nonspherical geometries that lead to increaseddifficulty of rolling along the channel roof. Moreover, bacteria andcells, with their complex surface chemistries, interacted with the PDMSchannel more strongly (resulting in more prevalent cellular attachment)than the bare microspheres, indicating potentially higher effectivekinetic friction coefficients between the cells and the PDMS surface.FIG. 5A depicts the spatially averaged linear velocity of cells andbacteria along the channel for an excitation frequency of 200 Hz. Thesmaller E. coli move continuously along the channel (velocity points inFIG. 5A do not cross zero) and eventually left the observation window,whereas blood cells were localized between electrodes velocity pointsreach zero). Note that the larger variation observable in the red bloodcell data FIG. 5A stems from a statistical fluctuation; there are only afew red blood cells that passed through a given x-location during theobservation window, and their nonspherical shapes mean that each cellwould be at a random angular orientation (and slightly differentinstantaneous velocity) as it rolled down the channel at that location.Bacteria, although varying in length and nonspherical, had enoughnumbers (several hundred through a given x-location) to result in goodaverage statistics. In the end, ≈6,750 of the 7,050 E. coli bacteriainitially present within the field of view of the sample were cleared(95.7% separation efficiency) within 45 s. Of the 1,018 red blood cellsinitially present, 954 were trapped, corresponding to a trappingefficiency of 93.7% and cell purity of 76.1%.

In a different experiment, healthy red blood cells were separated fromthose afflicted with sickle ceil anemia by exploiting the shape andelasticity differences between them (FIG. 5B). A blood sample containingapproximately a 4:1 ratio of healthy-to-sickle red blood cells was addedto the ferrofluid and introduced into the microchannel. At 300 Hz,sickle cells were trapped, whereas the healthy blood cells were clearedcontinuously from the channel (fluctuations in each dataset depicted inFIG. 5B are statistical in nature). In a sample initially containing≈501 healthy red blood cells and 145 sickle cells, 300 healthy cellswere cleared, whereas 109 sickle cells were trapped. Assuming that thegoal is to clear the sample from sickle cells, these numbers correspondto a separation efficiency of 75.2% (109 of 145 sickle cells wereseparated from healthy ones) and a healthy cell purity of 89.3% (300healthy cells and 36 sickle cells were cleared).

These Examples demonstrate the use of ferromicrofluidics insignificantly reducing incubation times and increasing diagnosticsensitivity in cellular assays through rapid separation and selectivedelivery of target cells to sensor arrays. While manipulation andseparation of microparticles and live cells within microfluidic devicesis also possible through established techniques (such as DEP andmagnetic label-based methods), the ferromicrofluidic approach of thepresent invention offers numerous advantages over existing methods. Forexample, target cells can be concentrated, trapped, localized, or simplydirected toward sensor surfaces efficiently, rapidly, and in alabel-free fashion. The biocompatible ferrofluid of the presentinvention can sustain live blood cells for several hours withoutdeterioration in physical properties, allowing extended examination ofthe target sample.

When combined with a simple photodiode, ferromicrofluidic separation ofcells can provide a rapid, automated, and disposable blood assay thatcan count and estimate the concentration of any target cell type (suchas bacteria or sickle cells) within 1 min, without the need for amicroscope, pumps, or lengthy sample, preparation steps. The presentinvention can also be used to selectively concentrate rare cells, suchas circulating tumor cells in blood samples, by exploding thedifferences in Young's modulus of the subject cell types (Lekka et al.,1999, Eur Biophys J 28:312-316). Applied in this manner, the presentinvention can increase detection sensitivity of existing cellularassays.

The present invention thus includes a cellular manipulation andseparation platform using biocompatible ferrofluids within lowcostmicrofluidic devices. We have demonstrated highly efficient particleseparation that is achievable in <1 min. As an example, bacteria can beseparated from live blood cells, and sickle cells can be separated fromhealthy red blood cells. In the case of a flow-based device, separationcan be achieved with particle manipulation perpendicular to the flowdirection. By varying electrode geometry and input excitation frequency,the devices of the present invention can be tailored for different sizeranges of particles and cells. Together with control of microchannelsurface chemistry, the present invention can be integrated withinlab-on-a-chip sensors and diagnostic systems to direct target cellstoward active regions. In this manner, the present invention cansignificantly reduce incubation times and increase the practicaldetection sensitivities achieved in existing sensors and diagnosticplatforms.

The disclosures of each and every patent, patent application, andpublication cited herein are hereby incorporated herein by reference intheir entirety.

While this invention has been disclosed with reference to specificembodiments, it is apparent that other embodiments and variations ofthis invention may be devised by others skilled in the art withoutdeparting from the true spirit and scope of the invention. The appendedclaims are intended to be construed to include all such embodiments andequivalent variations.

What is claimed:
 1. A device for separating a sample of particlessuspended in a biocompatible ferrofluid, comprising: a microfluidicchannel having a sample inlet, at least one output, and a length betweenthe sample inlet and the at least one output, wherein a sample can beadded to the sample inlet and flow along the length to the at least oneoutlet; a plurality of electrodes, wherein the microfluidic channellength transverses at least a portion of the plurality of electrodes;and a power source for applying a current to the plurality of electrodesto create a magnetic field pattern along the length of the microfluidicchannel.
 2. The device of claim 1, wherein the spacing betweenelectrodes is gradually increased.
 3. The device of claim 1, wherein thespacing between electrodes is gradually decreased.
 4. The device ofclaim 1, wherein the plurality of electrodes comprise at least oneelectrode layer.
 5. The device of claim 4, wherein the plurality ofelectrodes comprise a plurality of electrode layers.
 6. The device ofclaim 5, wherein the plurality of electrode layers is in a substantiallyorthogonal pattern.
 7. The device of claim 1, wherein the plurality ofelectrodes comprise a pattern of concentric circles.
 8. The device ofclaim 1, wherein the walls of the microfluidic channel length include apocketed, a ridged, a grooved, a trenched or a sloped region.
 9. Thedevice of claim 1, wherein the microfluidic channel length transversesat least a portion of the plurality of electrodes at an angle betweenabout 1-90 degrees.
 10. The device of claim 1, wherein the particles areliving cells.
 11. A system for separating at least one target from asample suspended in a biocompatible ferrofluid, comprising: amicrofluidic channel having a sample inlet, at least one output, and alength between the sample inlet and the at least one output, wherein asample can be added to the sample inlet and flow along the length to theat least one outlet; a plurality of electrodes, wherein the microfluidicchannel length transverses at least a portion of the plurality ofelectrodes, and generating a magnetic field pattern along the length ofthe microfluidic channel when a current is applied to the electrodes;and at least one target in a sample suspended in a biocompatibleferrofluid; wherein the at least one target is separated from theremaining sample as the at least one target passes along at least aportion of the microfluidic channel length.
 12. The system of claim 11,wherein the sample comprises living cells.
 13. The system of claim 12,wherein the biocompatible ferrofluid comprises a suitable amount ofionic species to control the osmotic pressure on the cells to promotecell sustainability.
 14. The system of claim 13, wherein thebiocompatible ferrofluid comprises a citrate concentration of betweenabout 5-200 mM.
 15. The system of claim 14, wherein the biocompatibleferrofluid comprises a citrate concentration of about 40 mM.
 16. Thesystem of claim 12, wherein the biocompatible ferrofluid has a pH ofabout 7.4.
 17. The system of claim 11, wherein the at least one targetis separated based on target size.
 18. The system of claim 11, whereinthe at least one target is separated based on target shape.
 19. Thesystem of claim 11, wherein the at least one target is separated basedon target elasticity.
 20. The system of claim 11, wherein the spacingbetween electrodes is gradually increased.
 21. The system of claim 11,wherein the spacing between electrodes is gradually decreased.
 22. Thesystem of claim 11, wherein the target is separated by being directed toa selected outlet.
 23. The system of claim 11, wherein the target istrapped based on the spacing of electrodes.
 24. The system of claim 11,wherein the at least one target is a cell.
 25. The system of claim 11,wherein the at least one target is a particle.
 26. The system of claim11, wherein the plurality of electrodes comprise at least one electrodelayer.
 27. The system of claim 11, wherein the plurality of electrodescomprise a plurality of electrode layers.
 28. The system of claim 27,wherein the plurality of electrode layers is in a substantiallyorthogonal pattern.
 29. The system of claim 11, wherein the plurality ofelectrodes comprise a pattern of concentric circles.
 30. The system ofclaim 11, wherein the walls of the microfluidic channel length include apocketed, a ridged, a grooved, a trenched or a sloped region.
 31. Thesystem of claim 11, wherein the microfluidic channel length transversesat least a portion of the plurality of electrodes at an angle betweenabout 1-90 degrees.
 32. A method for separating at least one cell type,comprising: suspending two or more cell types in a biocompatibleferrofluid to form a sample; passing the sample through a microfluidicchannel that transverses a plurality of electrodes; applying a currentto the plurality of electrodes to create a magnetic field pattern alongthe length of the microfluidic channel; and sorting the ceils into atleast one output channel based on a variation of at least one of cellsize, shape and elasticity.
 33. The method of claim 32, wherein thebiocompatible ferrofluid comprises a suitable amount of ionic species tocontrol the osmotic pressure on the cells to promote cellsustainability.
 34. The method of claim 33, wherein the biocompatibleferrofluid comprises a citrate concentration of between about 5-200 mM.35. The method of claim 34, wherein the biocompatible ferrofluidcomprises a citrate concentration of about 40 mM.
 36. The method ofclaim 33, wherein the biocompatible ferrofluid has a pH of about 7.4.37. The method of claim 32, wherein the separated cells are beingdirected to a selected outlet.
 38. The method of claim 32, wherein theseparated cells are being trapped based on the spacing of electrodes.39. The method of claim 32, wherein the cells are separated at anefficiency of at least about 90%.
 40. The method of claim 32, whereinthe size resolution in separating is iess than about 10 μm.
 41. Themethod of claim 32, wherein the cells are separated in iess than about 1minute.